For the following two problems, write a system of linear equations that determines the loop currents. You don't need to reduce the matrix. You can reduce it if you want but it will take forever. More problems: 5-8 section 1.10 1. WV 30 V - I1 12 - 30 V Is 4 20 V - Wv M 40 2. In a certain Region, about 7% of a city's population moves to the surrounding suburbs each year, and about 5% of the suburban population moves into the city. In 2010, there were 800,000 residents in the city and 500,000 in the suburbs. Set up a difference equation that describes this situation, where To is the initial population in 2010. Then estimate the populations in the city and in the suburbs two years later, in 2012. More problems: 9-11 section 1.10 3. Compute each matrix sum or product if it is defined. If an expression is undefined, explain why. Let E= (a) A - 2B (b) 5E - C (c) DB (d) EC More problems: 1-2 section 2.1 4. Compute the product AB in two ways: (a) by the definition, where Abj and Ab, are computed separately, and (b) by the row-column rule for computing AB More problems: 5-6 section 2.15. Find the inverses of the matrices or show that they do not exist. -3 A = B = 3 6 More problems: 1-4 section 2.2 6. Use the inverse of the matrix [ ] ] to solve the system More problems: 5-6 section 2.2 3r1 + 202 = 1 7. Use the algorithm introduced in section 2.2 to find the inverse, if it exists, of the following matrix. -2 -3 -3 -3 1 More problems: 29-32 section 2.2 -2 -4